Stochastic Reduced-Order Models for Calculating Response Statistics of Structural Systems Subjected to Random Input

Abstract

Abstract. Probabilistic characterization of a system's response under random dynamic input is essential for performance-based engineering. Monte Carlo simulation is the only general method available for estimating response statistics. However, the method is computationally expensive for realistic structural systems since it involves repeated deterministic dynamic analyses for a large number of samples of the random input. The framework of random vibration is also inadequate for calculating response statistics for linear systems under non-Gaussian inputs and non-linear systems subjected to both Gaussian and non-Gaussian excitation.We propose a novel, highly efficient method for calculating response statistics. The method is based on stochastic reduced-order models (SROM), i.e., stochastic processes that have a finite number of samples selected in an optimal manner from samples of the input process. The SROM-based method can be viewed as a smart Monte-Carlo. Like Monte-Carlo simulation, the method uses random samples of the input to characterize structural response. Unlike Monte Carlo, which uses a large number of samples selected at random, SROM selects just a small number of samples in an optimal way. Numerical examples of the newly proposed method are presented for single-degree-of-freedom linear and non-linear Duffing and Bouc-Wen systems.1342